Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse

Abstract

We extend the persistent homology analysis of~\paperone{} to the full Roman--Byzantine trade network (0--1453\,\textsc{ce}), using 2{,}599 nodes and 4{,}503 trimodal edges calibrated against the \textsc{orbis} Geospatial Network Model. Five results are reported. % (i)~The $H_t=0$ western sub-network result of~\paperone{} is a data-coverage artifact: with full western representation ($N_{\mathrm{west}}=987$, ${\beta }_1\approx 52$ cycles per decade) a baseline East--West entropy gap of $+2.22$ units is present from 0\,\textsc{ce} and grows at $+3.3\times 10^{-3}$\,yr${}^{-1}$, predating the Theodosian partition by four centuries. % (ii)~A \emph{hub-selection artifact} in degree-heterogeneous networks can reverse the sign of the inferred Phase~III slope, requiring full-coverage or stratified sampling for reliable structural-break detection. % (iii)~Decomposing Byzantine resilience into geographic ($H_{\mathrm{geo}}$) and economic ($H_{\mathrm{eco}}$) components reveals a peak decoupling ratio $R_d=H_{\mathrm{eco}}/H_{\mathrm{geo}}=47.7$ at 620\,\textsc{ce}, falling to 13.9 at 640\,\textsc{ce}, quantifying the McCormick--Ward-Perkins historiographical debate as a contrast between two network layers operating on different timescales. % (iv)~The inter-decade $W_2$ Wasserstein velocity identifies the Late Roman--Early Byzantine transition (495\,\textsc{ce}) as the highest topological-velocity event of the 1,453-year record; the cross-network Wasserstein ratio increases by $150$--$300\times$ after the Chrysobull of 1082\,\textsc{ce}, providing an independent diagram-space analogue of $R_d$. Both the Western collapse (476\,\textsc{ce}) and the Byzantine endpoint (1453\,\textsc{ce}) occur at $H^{\ast }\approx 0.524$, interpreted as a candidate topological percolation threshold.

26 pages and 6 figures